Abstract
In this work we study the some general fractal sums of pulses defined in ℝ by:
where (a n ), (λ n ) two positive scalar sequences such that ∑a n is divergent, and (λ n ) is non-increasing to 0, G is an elementary bump and X n are independent random variables uniformly distributed on a sufficiently large domain Ω. We investigate the Hausdorff dimension of the graph of G and in particular we answer a question given by Tricot in (Courbes et dimensions fractales, Springer, Berlin, 1995).
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de Amo, E., Bhouri, I. & Fernández-Sánchez, J. A note on the Hausdorff dimension of general sums of pulses graphs. Rend. Circ. Mat. Palermo 60, 469–476 (2011). https://doi.org/10.1007/s12215-011-0061-3
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DOI: https://doi.org/10.1007/s12215-011-0061-3